Abstract
A model has been proposed of the homogenization of a transversally-isotropic composite material, whose mechanical characteristics differ at the longitudinal stretching and compression. On its basis, the longitudinal elasticity module of the first kind has been derived, as well as a Poisson coefficient for a multimodular composite. These indicators are necessary to design structural elements made from composites. The object of the study is a unidirectional fibrous composite consisting of the isotropic elastic matrix and fibers. To determine the effective elastic constants, an approach has been suggested, which is based on the use of conditions for the alignment of the displacements of points in the homogenized composite, matrix, and fiber. First, the displacements and stresses are determined for the matrix and fiber points at their joint axisymmetric stretching. An equation from the multimodular theory of elasticity was preliminarily obtained for solving this problem. Similar components of the stressed-strained state are determined at the same deformation of the cylindrical cell made from a homogeneous transversally-isotropic composite. The conditions for the displacement alignment, derived in solving the specified problems, are the equality of axial displacements in an arbitrary cross-section of the composite by a plane, parallel to the isotropy plane, and the radial displacements at the surface of the composite cell. The result of applying these conditions is the derived formulae for effective constants – the longitudinal module of elasticity of the first kind and a Poisson coefficient, which express these indicators through the mechanical characteristics of the matrix and fiber, as well as the proportion of fibers in the composite cell volume. Similar formulae have been obtained for the longitudinal compression. The derived effective elastic characteristics of a transversally-isotropic composite could be used when calculating the stressed-strained state of the structural elements made from it. In this case, one takes into consideration differences in the values of stresses and deformations under axial stretching and compression
Highlights
Requirements of technological progress give rise to the need to create new structural materials, among which an important place belongs to composites
We suggest a procedure for determining the effective elastic constants for a transversally-isotropic multi-modular fibrous composite at stretching and compression, which is based on the application of the kinematic conditions for aligning the displacements of the composite and its components
We have proposed a procedure for the homogenization of a transversally-isotropic fibrous multimodular composite, based on using the kinematic conditions for the alignment of the axial and radial displacements of a composite and its components
Summary
Requirements of technological progress give rise to the need to create new structural materials, among which an important place belongs to composites. It is impossible to calculate the stressed-strained state of a fibrous composite as a fiber system reinforced by a matrix because of the huge number of such inclusions. In this regard, there is a need for the homogenization of a composite material. Modern technology widely employs those composites whose physical-mechanical characteristics differ at stretching and compression Such materials are called multimodular (bimodular) because their elastic constants that relate the stresses and deformations accept different values at stretching and compression. The knowledge of the effective elastic constants for multi-modular composites would solve the task of determining the components of their stressed-strained state, which could create possibilities for successfully applying these materials in practice. It is a relevant task to undertake a study aimed at deriving their effective mechanical characteristics
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Eastern-European Journal of Enterprise Technologies
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
